Generally speaking, radionavigation signals transmitted by satellites (or pseudolites) of a positioning system are in the form of a carrier modulated by a type of spreading waveform containing a pseudo-random binary code (“spreading code”). As the modulation of the carrier causes the spreading of the spectrum around the carrier frequency, the radionavigation signals are often called “in spread-spectrum”. The pseudo-random codes represent a signal identifier and therefore an identifier of the transmitting satellite. When known to the receivers, they enable the receivers with a code division multiple access (CDMA). Secondarily, certain satellite positioning signals can also transport useful data (e.g. the navigation message) in the form of a binary sequence (at a markedly lower rate than the pseudo-random code) also modulated on the carrier. In the following we will neglect this useful data load.
In the case of Global Positioning System (GPS), the radionavigation signals are transmitted in the frequency bands L1, centred on 1575.42 MHz and L2, centred on 1227.6 MHz. The band L5, centred on 1176.45 MHz, will be added when the GPS is updated. The satellites of the Galileo constellation will transmit in the bands E2-L1-E1 (the portion of the middle band L1 being the same as that of GPS), E5a (which, pursuant to the Galileo nomenclature, represents the band L5 destined for GPS), E5b (centred on 1207.14 MHz) and E6 (centred on 1278.75 MHz). The satellites of the Compass constellation transmit or will transmit in the band B1 (centred on 1561.098 MHz), B1-2 (centred on 1589.742 MHz), L1 (centred on 1575.42 MHz), B2 (centred on 1207.14 MHz) and B3 (centred on 1268.52 MHz). The central frequencies represent the frequencies of the carriers of the different signals.
The reception of a radionavigation signal normally comprises a first demodulation with the help of an internal replica of the carrier generated in the receiver by an oscillator commanded by a carrier tracking loop and a second demodulation with the help of an internal replica of the spreading waveform (the “replica code”) produced by a waveform generator commanded by a spreading waveform tracking loop (also called “code tracking loop”). The feedback signals from the carrier tracking and spreading waveform loops are used by the receiver to determine its position. The continuation principally concerns the observable of code, i.e. the time lag signal between the spreading waveform of the received signal and the internal replica of the spreading waveform produced at each epoch by the tracking loop of the spreading waveform. It should be noted however that a carrier tracking loop is used to compensate for the Doppler effect.
The code and carrier internal replicas are mixed (multiplied) with the entering radionavigation signal, after this has been filtered, amplified transposed in frequency as well as digitised. The mixed products are then integrated, thereby realising, broadly speaking, an operation of correlation between the internal replicas and the entering signal. In radionavigation signal reception one usually distinguishes between two phases: the “acquisition” phase and the “tracking” phase. In the acquisition phase one attempts to synchronise the internal replica of the code on the entering radionavigation signal (in other words, one attempts to measure the code delay) as well as the Doppler frequency of the entering radionavigation signal. Therefore, in principle, the search area is a two-dimensional space, in which one seeks the values of the code delay and the Doppler frequency shift, which maximise the correlation function. (In practice, the signal is considered to have been acquired if the correlation exceeds a specific threshold value.)
Certain radionavigation signals use modulations having recourse to a form of spreading wave, in which the pseudo-random binary code is multiplied by a binary sequence having a higher rate than the code. Hereinafter, such modulations will be called “sub-carrier modulations”. The binary sequence with a higher rate will be considered as the sub-carrier, which is justified by the fact that the density of the spectral energy of such a signal has two principal lobes that are at a distance from the carrier frequency by a spectral deviation equivalent to the central frequency (sub-carrier frequency) of the binary sequence. Some examples of these modulations are the binary coded symbol (BCS) modulations and the binary offset carrier (BOC) modulations, which in fact represent specific BCS modulations. Generally speaking, BOC(n,m) is a function of time t defined by:BOC(n,m)(t)=Cm(t)·sign[sin(2πfsct)],  (Eq. 1)                where Cm(t) is a pseudo-random binary code with a chip rate m×1.023 Mcps (mega chips per second, i.e. 106 chips per second) taking the values +1 or −1 and fsc is the sub-carrier frequency n×1.023 MHz. A condition for n and m is that the ratio 2n/m is a whole number. In the case of the OS (open service) of Galileo, the chip rate is fixed at 1.023 Mcps (mega-chips per second). The “sub-carrier BOC” is understood to mean the BOC waveform without the code, i.e. the part sign[sin(2πfsct)]. Remark: if the sinus in the right hand side of the equation 1 is replaced by a cosinus, then the quadrature of the function BOC, called BOCc, is obtained:BOCc(n,m)(t)=Cm(t)·sign[cos(2πfsct)].  (Eq. 2)The “sub-carrier BOCc” is understood to mean the BOC waveform without the code, i.e. the part sign[cos(2πfsct)].        
More generally, the waveform in quadrature phase of a spreading waveform BCS is obtained by cyclically shifting the sequences of symbols by a half symbol.
The sub-carrier modulations referred to above have certain advantages over the classical binary phase shift keying (BPSK) modulations, notably in the precision of the measurement of position obtained based on the code observables. However, the sub-carrier spreading waveforms also have some drawbacks, because their acquisition and tracking are more difficult to realise than e.g. the acquisition and tracking of a signal of the BPSK type. This can be explained with the help of auto-correlation functions. The auto-correlation function of a BPSK modulation has only a single extremum (for a time lag of 0); that of a sub-carrier modulation exhibits oscillations and therefore a plurality of extrumums, onto which the tracking code loop can lock itself. In other words, a tracking code loop discriminator that exhibits a higher precision given by the sub-carrier will have the disadvantage of being ambiguous (in the sense that the delay between the spreading waveform of the received signal and its internal replica is potentially evaluated with respect to an incorrect peak of the correlation function).
The spreading codes normally exhibit a fixed periodicity of the order of several milliseconds, such as e.g. 1 ms (1023 chips) for the Gold codes used in the C/A signal of the GPS system or 4 ms (4092 chips) for the (primary) codes used in the case of the open service (OS) signal of Galileo. The methods for radionavigation signal acquisition modulated by such codes can therefore exploit the periodicity of the code. Document WO 2006/040325 A1, for example discloses an acquisition method utilising a “matched filter”, in which the spreading code in its entirety is sampled and loaded into a code register and the radionavigation signal is sampled in a signal register. At each clock cycle the signal correlation is calculated in the register and the code, and the sample signal is shifted in its register between two correlation operations. The code is not shifted.
Document WO 2004/034604 A1 discloses another acquisition method. In this method the spreading code is loaded by sampled segments into a code register and the radionavigation signal is sampled into a signal register. At each clock impulse the correlations between the code segments and the corresponding parts of the signal are calculated, thereby affording a plurality of short term correlations (STC). The sum of all the STCs is equal to the correlation between the entire code and the signal in the register. However, this sum is not calculated; it is rather the Fourier transform of the vector of the STC values. This Fourier transform enables the Doppler frequency to be detected. Between two correlation operations (calculation of the different STCs and associated steps for a given shift), the signal of a sample is shifted in its register, the code remaining fixed. Other acquisition methods are explained e.g. in the article “Signal acquisition and search, and antenna polarization”, published in Inside GNSS, March/April 2007, pp. 26-33.
Certain radionavigation signals carry spreading codes having a much longer periodicity (preferably at least 10 times, even 100 or 1000 times longer) than the correlation time (i.e. the time between the coherent integration limits that are part of the correlation operation). In the context of the present document, such codes will be called “with a quasi-infinite period”. The traditional acquisition methods described above are only partially applicable to the acquisition of radionavigation signals having spreading codes with a quasi-infinite period. If the period of the code is of the same order of magnitude as the correlation time (several milliseconds), then it suffices to load the code into a register and to calculate its correlation with the radionavigation signal for different shifts of the signal. In fact, if the signal carries the tested code, then one is certain to obtain a correlation peak at the latest when the signal will have been shifted by one period of code. If the same strategy is used to acquire signals that carry codes having a long period, then there is a risk of having to wait a considerable time before finding a correlation peak. Consequently, another acquisition strategy needs to be used for these signals.